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Obtaining information through the measurement of brain signals recorded during different processes or physiological conditions is important for developing computer interfaces that translate electrical brain signals to computer control commands. Electroencephalography (EEG) records the electrical activity of the brain in response to its receipt of different external stimuli (potential events). Analysis of these signals makes it possible to identify and distinguish specific states of physiological brain function. The Fractal Dimension has been used as a tool for biomedical waveform analysis, in particular to measure the complexity of time series generated by EEG. This paper aims to analyze a database (HeadIT) of biomedical time series obtained by EEG for which the fractal dimension will be obtained by the Higuchi, Katz and multiresolution box-counting methods, showing the relationship between the method for obtaining the fractal dimension and the physiological condition of the brain event-related potentials.
M. Bachmann, J. Lass, A. Suhhova and H. Hinrikus, (2013). Spectral asymmetry and Higuchi´s Fractal Dimension Measures of Depression Electrencephalogram, Computational and Mathematical Methods in Medicine, Hindawi Publishing Corporation, vol. 2013, 8 pages.
P. N. Baljekar and H. A. Patil, (2012). A comparison of waveform fractal dimension techniques for voice pathology classification, IEEE ICASPP ISSN 978-1-4673-0046-9, pp. 4461-4464
T. Bojić, A. Vuckovic, A. Kalauzi, (2010). Modeling EEG fractal dimension changes in wake and drowsy states in humans—a preliminary study, Journal of Theoretical Biology, 262, pp. 214-222.
A. Bashashati, R.K. Ward, G.E. Birch, M.R. Hashemi, MA. Khalilzadeh, (2003). Fractal Dimension-Based EEG Biofeedback System, Proceedings of the 25th Annual International Conference of the IEEE EMBS, pp. 2220-2223, 2003.
F. Cervantes-De la Torre, J.I. González-Trejo, C.A. Real-Ramirez and L.F. Hoyos-Reyes,(2013). Fractal dimension algorithms and their application to time series associated with natural phenomena, 4th National Meeting in Chaos, Comlex Sustem and Time Series, Journal o Physics: Conference Series, 475, 10 pages.
A. Delorme and S. Makeig, (2004). EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics. Journal of Neuroscience Methods, 134:9-21.
Dubravka R. Jevtić, and Milorad P. Paskaš, (2011). Application of Katz Algorithm for Fractal Dimension in Analysis of Room Impulse Response, 19th Telecommunications forum TELFOR 2011, pp. 1063-1066.
D. Easwaramoorthy and R. Uthayakumar, (2010). Analysis of EEG Signals using Advanced Generalized Fractal Dimensions, Second International conference on Computing, Communication and Networking Technologies, 978-1-4244-6589-7, 6 pages.
R. Esteller, G. Vachtsevanos, J. Echauz, and B. Litt, (2001). A Comparison of Waveform Fractal Dimension Algorithms, IEEE Transactions on Circuits and Systems-I: fundamental theory and applications, vol. 48, no. 2, pp. 177-183, 2001.
G. Gálvez Coyt, A. Muñoz Diosdado, J. A. Balderas López, J. L. del Rio Correa, and F. Angulo Brown, (2013). Higuchi’s Method applied to the detection of periodic components in time series and its application to seismograms, COMPLEX SYSTEMS Revista Méxicana de Física, S 59 (1), pp. 1-6.
S. Georgiev, Z. Minchev, C. Christova, D. Philipova, (2009). EEG Fractal Dimension Measurement before and after Human Auditory Stimulation, Bioautomaton, pp. 70-81.
B. P. Harne, (2014). Higuchi Fractal Dimension Analysis of EEG Signal before and after OM Chanting to Observe Overall Effect on Brain, International Journal of Electrical and Computer Engineering (IJECE), vol. 4 pp. 585-592.
HeadIT, Swartz Center for Computational Neuroscience (SCCN) of the University of California, San Diego. Its development has been funded by U.S. National Institutes of Health grants R01-MH084819 (Makeig, Grethe PIs) and R01-NS047293 (Makeig PI).
M. Katz, (1988). Fractals and the analysis of waveforms, Computers in Biology and Medicine, vol. 18, pp. 145-156.
T. Q. D. Khoa, V. Q. Ha and V. V. Toi, (2012). Higuchi Fractal Properties of Onset Epilepsy Electroencephalogram, Computational and Mathematical Methods in Medicine, Hindawi Publishing Corporation, vol. 2012, 6 pages.
C. K. Loo, A. Samraj and G. C. Lee, (2011). Evaluation of Methods for Estimating Fractal Dimension in Motor Imagery-Based Brain Computer Interface, Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society Vol. 2011, Article ID 724697, 8 pages.
W. Lutzenberger, H. Preissl, F. Pulvermüller, (1995). Fractal dimension of electroencephalographic time series and underlying brain processes, Biological Cybernetics Springer-Verlag, vol. 73, pp. 477-482.
S. Makeig, A. Delorme, M. Westerfield, T-P. Jung, J. Townsend, E. Courchesne and T. J. Sejnowski, (2004). Electroencephalographic brain dynamics following visual targets requiring manual responses, Public Library of Science Biology, 29 pages.
S. Makeig, M. Westerfield, T-P Jung, J. Covington, J. Townsend,T. J. Sejnowski, and E. Courchesne, (1999). Functionally Independent Components of the Late Positive Event-Related Potential during Visual Spatial Attention, The Journal of Neuroscience, 19 (7), pp. 2665-2680.
A. S. Martins, L. A. Neves, M. Z. Nascimento, M. F. Godoy, E. L. Flores and G. A. Carrijo, (2012). Multiscale Fractal Descriptors and Polynomial Classifier for Partial Pixels Identification in Regions of Interest of Mammographic Images, IEEE Latin America Transactions, Vol. 10, No. 4, pp. 1999-2005.
G. Millán, E. S. Juan and M. Jamett, (2014). Simple Estimator of the Hurst Exponent for Self-Similar Traffic Flows, IEEE Latin America Transactions, Vol. 12, No. 8, pp. 1341-1346.
Müller K.R., and Mattia D. (2010). Combining Brain-Computer Interfaces and Assistive Technologies: State-of-the-Art and Challenges. Frontiers in Neuroscience, Vol 4, pp.161.
H. H. Mueller, (2010) “QEEG Brain Mapping, Evaluating the rhythms of the Brain”, Edmonton Neurotherapy, 2010, On line
P. Paramanathan, R. Uthayakumar, (2008), Application of fractal theory in analysis of human electroencephalographic signals, Computers in Biology and Medicine, no. 38, pp. 372-378
P. Paramanathan and R. Uthayakumar, (2007). Detecting Patterns in Irregular Time Series with Fractal Dimension, International Conference on Computational Intelligence and Multimedia Applications, pp. 323-327.
F. R. Perlingeiro, L. L. Ling, (2005). Uma Nova Abordagem para Estimação da
Banda Efetiva em Processos Fractais. IEEE Latin America Transactions, Vol. 3, No. 5, pp. 436-446.
G. E. Polychronaki, P. Y. Ktonas, S. Gatzonis, A Siatouni, P. A. Asvestas, H. Tsekou, D. Sakas and K. S. Nikita, (2010). Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection, Journal of Neural Engineering, 046007, 18 pages.
B. S. Raghavendra, and D. N. Dutt, (2010). Computing Fractal Dimension of Signals using Multiresolution Box-counting Method, International Journal of Information and Mathematical Sciences, 6:1, pp. 50-65.
B. S. Raghavendra and D. N. Dutt, (2009). A note on fractal dimensions of biomedical waveforms, Computers in Biology and Medicine, 39, pp. 1006-1012.
S. Spasić, Lj. Nikolić, D. Mutavdžić, J. Šaponjić, (2011). Independent complexity patterns in single neuron activity induced by static magnetic field, Computer Methods and Programs in Biomedicine, vol. 104, pp. 212-218.
Sabogal S., Arenas G. (2011). Una Introducción a la geometría Fractal, Escuela de Matemáticas, Universidad Industrial de Santander. Bucaramanga, Cap I, pp. 2-15.